{"id":12708,"date":"2023-01-07T21:08:31","date_gmt":"2023-01-07T15:38:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=12708"},"modified":"2023-01-07T21:08:35","modified_gmt":"2023-01-07T15:38:35","slug":"the-distribution-below-gives-the-weights-of-30-students-of-a-class-find-the-median-weight-of-the-students","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-distribution-below-gives-the-weights-of-30-students-of-a-class-find-the-median-weight-of-the-students\/","title":{"rendered":"The distribution below gives the weights of 30 students of a class. Find the median weight of the students."},"content":{"rendered":"\n
Weight in (kg)<\/td> | 40 – 45<\/td> | 45 – 50<\/td> | 50 – 55<\/td> | 55 – 60<\/td> | 60 – 65<\/td> | 65 – 70<\/td> | 70 – 75<\/td><\/tr> | ||||||||||||||||||||||||
Number of students<\/td> | 2<\/td> | 3<\/td> | 8<\/td> | 6<\/td> | 6<\/td> | 3<\/td> | 2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nSolution :<\/h2>\n\n\n\nWe prepare the following table to compute the median :<\/p>\n\n\n\n We have : n = 30, So, \\(n\\over 2\\) = 15<\/p>\n\n\n\n The cumulative frequency just greater than \\(n\\over 2\\) is 19 and the corresponding the class is (55 – 60).<\/p>\n\n\n\n Thus, (55 – 60) is the median class such that \\(n\\over 2\\) = 15, l = 55, f = 6, cf = 13 and h = 5.<\/p>\n\n\n\n Substituting these values in the formula,<\/p>\n\n\n\n Median = l + (\\({n\\over 2} – cf\\over f\\))(h)<\/p>\n\n\n\n = 55 + (\\(15 – 13\\over 6\\))(5) = 55 + \\(2\\over 6\\)(5) = 55 + 1.67 = 56.67<\/p>\n\n\n\n Hence, the median weight is 56.67<\/strong> kg<\/p>\n","protected":false},"excerpt":{"rendered":" Question : Weight in (kg) 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 Number of students 2 3 8 6 6 3 2 Solution : We prepare the following table to compute the median : Weight in (kg) Number of students (frequency) …<\/p>\n |